{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "oil_Nodal.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyMxA9DnVpzuDW93PxBlZo2v",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Divyanshu-ISM/Oil-and-Gas-data-analysis/blob/master/oil_Nodal.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HbL3uTF851Sg",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "%matplotlib inline"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8SlGt-Ox6Go9",
        "colab_type": "text"
      },
      "source": [
        "#Vogel's IPR \n",
        "\n",
        "## data-\n",
        "\n",
        "Reservoir pressure = 3000 psia'\n",
        "\n",
        "Tested flowing bottom-hole pressure, pwf 1 = 2000 psia\n",
        "\n",
        "Tested production rate at pwf 1, q1 =500 stb=day\n",
        "\n",
        "Tested flowing bottom-hole pressure, pwf 2 = 1000 psia\n",
        "\n",
        "Tested production rate at pwf 2, q2 = 800 stb=day"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VuB_RUIc6Ddt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "b05e6449-de43-4004-b6d5-d6bd400981ff"
      },
      "source": [
        "Pres = float(input(\"Enter the reservoir pressure: \"))\n",
        "\n",
        "pwf1 = float(input(\"Enter the test pwf1: \"))\n",
        "q1 = float(input(\"Enter the test flow rate(at pwf1): \"))\n",
        "\n",
        "pwf2 = float(input(\"Enter the test pw2: \"))\n",
        "q2 = float(input(\"Enter the test flow rate(at pwf2): \"))\n",
        "\n",
        "\n"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Enter the reservoir pressure: 3000\n",
            "Enter the test pwf1: 2000\n",
            "Enter the test flow rate(at pwf1): 500\n",
            "Enter the test pw2: 1000\n",
            "Enter the test flow rate(at pwf2): 800\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dy6-FzLW8wkx",
        "colab_type": "text"
      },
      "source": [
        "#As per Vogel's equation:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2QYbpitV8be1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e6c4d123-55d8-4505-8af0-7aa98d46e69b"
      },
      "source": [
        "qmax = q1/(1 - 0.2*(pwf1/Pres) - 0.8*(pwf1/Pres)**2)\n",
        "qmax"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "978.2608695652175"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "siuvrn6O9xL9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "2e847e0a-bd34-47e6-ebe1-f292c0c9b2d2"
      },
      "source": [
        "J_star = (1.8*qmax)/Pres\n",
        "J_star"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5869565217391305"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "N_tww3Bn-BB0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "q = np.linspace(0,qmax,50)"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FvbRMNXa-UmZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "pwf = 0.125*Pres*((81 - 80*(q/qmax))**0.5 - 1)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U2V_GIh4-vQ9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "0c804560-07ea-46fe-c923-a1625208c399"
      },
      "source": [
        ""
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f62b85355f8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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XpvBKZjYX/3Uuv35rFbsPHve7PJEyK9OtFc0sDegKZAAJzrmd3lu7gATveRKQXeJjOV7b6dq/vo6JZpZpZpn5+fllKU+kyjRrWIc/XN2ROT+9mOHdknghYzv9/zqHB95fy/4jJ/wuT6TUSh0CZlYPeB242zl3sOR7LtCnVCEjzM65Kc65dOdcenx8fEV8pUilSY6N5s/XdGL2PQMY3CGRKfM20+/BOTwyawMHj5/0uzyRsypVCJhZLQIB8KJzbobXnOd185waN9jttecCKSU+nuy1na5dpMZLi6vLI9d34aO7+9OvTRyPzt5Iv7/MYfLcLI6dKPK7PJHTKs3ZQQY8Dax1zj1c4q23gVNn+IwF3irRfpN3llAv4IDXbTQTGGhmsd6ZRAO9NpGg0SahPo/f2J137+hLt+YNefDD9Qz46xz+vWAbJ4uK/S5P5BtKc3ZQX2AesBI49a/45wTGBV4BmgPbgBHOuX1eaPyTwKDvUWCccy7T+67x3mcB/uice/ZM69bZQVLTLdq6jwc/XMeirftJbRzNPZefx/c6NdO0l1KpdLGYSDVyanKbB2euZ+3Og7RNbMC9V5zHJec3IfA3k0jFqtBTREWkfMyMSy5ownt39OXRkV04eqKQ8VMzuX7KApZsP+1lMiJVQiEgUkXCwoyhXZL4+J4B/P7qDmzOP8LwyV9w6wuL2ZR/2O/yJESpO0jEJ0cKCvnXvC1M+WwTxwuLuf7CFO6+rA1NGmhiGykfjQmI1CB7Dhfwj9kbeTFjO7XCw7i5XwsmDmhFvdoRfpcmNZRCQKQG2rb3CA/OXM97K3YSV68291x+HiPSk4kIV6+tlI0GhkVqoNTGdXlsdDfe+NFFtIiL5udvrGTQo/P4ZF0e1fmPNanZFAIi1UzX5rG88sPePHFjd4qKHeOnZjL6qQxW5R7wuzQJQgoBkWrIzBjUoSkf/bg/v72qPevzDvG9f37Ova8u191KpUIpBESqsVrhYYy9KI05P72Ym/u15M1luVz80Fz+MXsjx0/qnkRSfgoBkRogpk4tfj6kLR/fM4D+beL526wNXPrQXN5alqvxAikXhYBIDZLauC5PjOnO9Im9iK0byV3TlzH88S9Ynv2V36VJDaUQEKmBerVszNu39+XBazuRve8YQx+bHxgvOKTxAikbhYBIDRUeZoxIT2HOTwfww/6B8YJLH/qUJz/dxIlC3bZaSkchIFLD1Y+qxf1D2jLz7v70bNGIBz5YxxV//4xP1uX5XZrUAAoBkSDRMr4eT3//QqaOuxAzGD81kwlTF7F971G/S5NqTCEgEmQuPr8JH97Vn58PuYAFm/fynUc+5eFZG3RKqXwrhYBIEIqMCGNi/1bM/snFDGrflEmzN/Kdhz/lo9W7dEqp/A+FgEgQaxoTxaRRXZl2cy+iI8OZ+O/FjJu6iG17j/hdmlQTCgGRENC7VWPeu7Mfv7qyHZlb9zPwkc+YNHsjBYXqIgp1CgGREFErPIwJfVsw+ycD+E67BB6etYHBf5/H/Kw9fpcmPlIIiISYhAZRPDa6G8+P70GRc9zwrwzumr5UF5qFKIWASIjqf148M+/uz52XteGDlbu47G+f8sKCbRQXa+A4lCgEREJYVK1w7rn8PD68ux8dk2L45ZuruO7JL9mQd8jv0qSKKAREhJbx9XjxBz156LrObMo/zHcnzePhj9br2oIQcNYQMLNnzGy3ma0q0fYbM8s1s2XeY0iJ9+43sywzW29mV5RoH+S1ZZnZfRW/KSJSHmbGtd2TmX3PAK7s1IxJn2QxZNI8Fmze63dpUolKcyQwFRj0Le2POOe6eI/3AcysHTASaO99ZrKZhZtZOPAYMBhoB4zylhWRaqZxvdo8cn0Xnh/fg5NFxYycsoD7Z6zg4PGTfpcmleCsIeCc+wzYV8rvGwpMd84VOOe2AFlAD++R5Zzb7Jw7AUz3lhWRaqr/efF8dPcAJvZvycuLshn48GfMXqub0gWb8owJ3G5mK7zuolivLQnILrFMjtd2uvZvMLOJZpZpZpn5+fnlKE9EyqtOZDg/H9KWN37Uh5g6tZjwXCZ3T1/KviMn/C5NKsi5hsDjQCugC7AT+FtFFeScm+KcS3fOpcfHx1fU14pIOXROacg7d/Tlrsva8O6KnVz+8Ke8t2Kn7kMUBM4pBJxzec65IudcMfAUge4egFwgpcSiyV7b6dpFpIaIjAjjx5efxzt39KVZwzrc9tISbn1hCXsOF/hdmpTDOYWAmSWWeDkMOHXm0NvASDOrbWYtgDbAQmAR0MbMWphZJIHB47fPvWwR8UvbxAa88aOL+NmgC/hk3W4GPvIZ76/c6XdZco5Kc4roNOBL4HwzyzGzCcCDZrbSzFYAlwA/BnDOrQZeAdYAHwK3eUcMhcDtwExgLfCKt6yI1EAR4WHcenEr3r2zL0kN6/CjF5dw57SlfHVUYwU1jVXnPr309HSXmZnpdxkicgYni4p5fO4mJs3eSGzdSP48vCOXtU3wu6yQZmaLnXPppVlWVwyLSLnUCg/jzsva8NbtfWhcN5IJz2Vy76vLOaTrCmoEhYCIVIj2zWJ4+/a+3HZJK15fksPgR+exaGtpLzESvygERKTCREaEce8VF/DqLb0JM+P6J7/krzPXcaKw2O/S5DQUAiJS4bqnNuL9u/pxbfdkHpuziWse/4Ks3Yf9Lku+hUJARCpFvdoRPHhtZ564sTs5+49y5T/m8e8vt+oCs2pGISAilWpQh6bMvLs/PVs05ldvrebm5xezX7edqDYUAiJS6Zo0iGLquAv5f1e247MN+Qx+VLeori4UAiJSJcyM8X1bMONHF1EnMpzRTy3g4VkbKCzSoLGfFAIiUqU6JMXw7h19GdY1mUmzNzL6qQx2fHXM77JClkJARKpc3doR/G1EZ/5+fRdW7zjA4EfnMWuN5irwg0JARHxzddck3ruzH80bRXPz85k88MFadQ9VMYWAiPgqLa4ur97Smxt7NefJTzcz+qkM8g4e97uskKEQEBHfRdUK5w9Xd+TRkV1YteMA3500j/lZe/wuKyQoBESk2hjaJYm3b+9DbHQkNz6dwaTZGyku1sVllUkhICLVSusm9Xnr9j4M65LEw7M2MP65RRw4qjuSVhaFgIhUO9GRgbOH/jisA/Oz9nDVY5+zftchv8sKSgoBEamWzIwbeqYyfWIvjp4oYtjk+ZrGshIoBESkWuue2oh37+jL+U3r86MXl/Dgh+so0jhBhVEIiEi1l9AgiukTezGqRwqT525i/FSNE1QUhYCI1Ai1I8J5YHgn/jSsI19s2sPQxz7XHAUVQCEgIjXK6J7NmXZzLw4dL2TY5Pl8vlHXE5SHQkBEapz0tEa8eVsfEmOiGPvsQl5YsM3vkmoshYCI1EgpjaJ5/daL6Ncmjl++uYrfvrNaA8bnQCEgIjVW/aha/OumdMb1SePZ+Vv5wXOLOHRcA8ZlcdYQMLNnzGy3ma0q0dbIzGaZ2UbvZ6zXbmY2ycyyzGyFmXUr8Zmx3vIbzWxs5WyOiISaiPAwfv299vzh6g58tnEP1z7+peYnKIPSHAlMBQZ9re0+YLZzrg0w23sNMBho4z0mAo9DIDSAXwM9gR7Ar08Fh4hIRbixVyrPjevBjq+OMXzyF7rCuJTOGgLOuc+AfV9rHgo85z1/Dri6RPvzLmAB0NDMEoErgFnOuX3Ouf3ALL4ZLCIi5dK3TRwv/7A3xc5x7RNfaB7jUjjXMYEE59yp67d3AQne8yQgu8RyOV7b6dq/wcwmmlmmmWXm5+efY3kiEqraNWvAjB9dREKDKG56eiHvrdCtJs6k3APDzjkHVNiQvHNuinMu3TmXHh8fX1FfKyIhJDk2mtdu6U2n5Bhun7aEqfO3+F1StXWuIZDndfPg/dzttecCKSWWS/baTtcuIlIpGkZH8sIPejKwXQK/eWcND3ywVnMTfItzDYG3gVNn+IwF3irRfpN3llAv4IDXbTQTGGhmsd6A8ECvTUSk0kTVCmfyDd0Z0yuVJz/dzP0zVupagq+JONsCZjYNuBiIM7McAmf5/Bl4xcwmANuAEd7i7wNDgCzgKDAOwDm3z8x+Dyzylvudc+7rg80iIhUuPMz43dD2xNaNZNLsjRw9WcTDIzpTK1yXSUEpQsA5N+o0b132Lcs64LbTfM8zwDNlqk5EpAKYGfdcfh7RkeH8+YN1HDtRxD9HdyWqVrjfpflOUSgiIeOWAa34/dD2fLw2j5ufz+ToiUK/S/KdQkBEQsqY3mk8dF1n5mftYewzC0P+NhMKAREJOdd2T2bSqK4s3f4VN/wrg/1HTvhdkm8UAiISkq7s1Iwnx3Rn3a5D3Ph0RsjOVKYQEJGQdVnbBJ4c052NeYe56dnQ7BpSCIhISLvk/CY8dkM3Vuce4PvPLuJIQWgNFisERCTkXd4ugUmjurIs+ysmPLeIYyeK/C6pyigERESAIR0TeXhEZzK27GPivzM5fjI0gkAhICLiGdoliQev6cS8jXu49YXFFBQGfxAoBERESrguPYU/DevInPX53DVtWdDfa0ghICLyNaN7NudXV7bjw9W7+O07qwncESc4nfXeQSIioWhC3xbsOnCMp+ZtITGmDrde3MrvkiqFQkBE5DTuH9yWXQcL+MuH62gaU5thXZP9LqnCKQRERE4jLMx46LpO7DlUwL2vriC+XhR928T5XVaF0piAiMgZ1I4I54kx3WndpB63vLCY1TsO+F1ShVIIiIicRUydWkwd14MGURF8/9lF5Ow/6ndJFUYhICJSCk1jopg6vgcFJ4v4/rOLguY+QwoBEZFSOi+hPk+M6c6WPUf4ySvLg2LieoWAiEgZXNQqjl8MactHa/J4bE6W3+WUm0JARKSMxvVJ4+ouzXj44w3MWbfb73LKRSEgIlJGZsYDwzvRtmkD7py+lK17jvhd0jlTCIiInIM6keE8OaY74WHGxH9n1th5CBQCIiLnKKVRNP8c1Y2s3Ye597XlNfIeQwoBEZFy6Nsmjp8NuoD3V+7iiU83+11OmZUrBMxsq5mtNLNlZpbptTUys1lmttH7Geu1m5lNMrMsM1thZt0qYgNERPw2sX9Lvtspkb/OXMfCLfv8LqdMKuJI4BLnXBfnXLr3+j5gtnOuDTDbew0wGGjjPSYCj1fAukVEfGdmPHhNJ5Jjo/nJq8s4XIPGByqjO2go8Jz3/Dng6hLtz7uABUBDM0ushPWLiFS5urUjeHhEZ3L3H+P376zxu5xSK28IOOAjM1tsZhO9tgTn3E7v+S4gwXueBGSX+GyO1/Y/zGyimWWaWWZ+fn45yxMRqTrpaY344YBWvJyZzUerd/ldTqmUNwT6Oue6Eejquc3M+pd80wWGyss0XO6cm+KcS3fOpcfHx5ezPBGRqvXj75xH28QG3D9jJXsOF/hdzlmVKwScc7nez93AG0APIO9UN4/389TldLlASomPJ3ttIiJBIzIijL9f34VDxwu5f8bKan/a6DmHgJnVNbP6p54DA4FVwNvAWG+xscBb3vO3gZu8s4R6AQdKdBuJiASN85vW594rzmfWmjxeXZzjdzlnVJ6ZxRKAN8zs1Pe85Jz70MwWAa+Y2QRgGzDCW/59YAiQBRwFxpVj3SIi1dqEvi34eG0ev3tnDb1bNialUbTfJX0rq86HKunp6S4zM9PvMkREzknO/qMM+vs82iU2YNrEXoSHWZWs18wWlzht/4x0xbCISCVJjo3mN1e1Z+HWfbyYsc3vcr6VQkBEpBJd0y2J3i0b88isDRw4Wv1mI1MIiIhUIjPjl1e25atjJ5n0yUa/y/kGhYCISCVr3yyG69NTeP7LrWypZnMPKARERKrAPQPPIzI8jD+9v9bvUv6HQkBEpAo0qR/FbZe2ZtaaPL7I2uN3Of+hEBARqSLj+7QgObYOv3t3DUXF1eP0fIWAiEgViaoVzn2DL2DdrkO8mpl99g9UAYWAiEgV+m7HRNJTY3noo/UcOu7/KaMKARGRKmRm/OrKduw5fILJczf5XY5CQESkqnVOacjwbkk8/fkWsvcd9bUWhYCIiA/+74oLCDP4h88XkCkERER80DQmimFdk3h7+Q4OHPNvbEAhICLik9E9Ujl+spg3l/o3v5ZCQETEJx2TY+iUHFxPr3gAAAX5SURBVMNLGdt9m4FMISAi4qPRPZqzPu8Qi7ft92X9CgERER99r3Mz6teO4KWM7b6sXyEgIuKjurUjuLprEu+u3MlXR09U+foVAiIiPhvdszknCot5zYdJ6RUCIiI+a5vYgG7NG/LSwqofIFYIiIhUA6N7prI5/wgLNu+r0vUqBEREqoErOyXSICqClxZW7QCxQkBEpBqIqhXONd2T+XDVTvYcLqiy9SoERESqiRt6NudkkavSAeIqDwEzG2Rm680sy8zuq+r1i4hUV62b1KdHWiOmLdxOcRXNPFalIWBm4cBjwGCgHTDKzNpVZQ0iItXZDb2as23vUb7YtLdK1lfVRwI9gCzn3Gbn3AlgOjC0imsQEam2BnVoSmx0LV7M2FYl66vqEEgCSk6smeO1/YeZTTSzTDPLzM/Pr9LiRET8VjsinB/0a0mr+HpVcs1ARKWvoYycc1OAKQDp6en+3FZPRMRHt13SusrWVdVHArlASonXyV6biIj4oKpDYBHQxsxamFkkMBJ4u4prEBERT5V2BznnCs3sdmAmEA4845xbXZU1iIjIf1X5mIBz7n3g/aper4iIfJOuGBYRCWEKARGREKYQEBEJYQoBEZEQZlU9i01ZmFk+UJ5rp+OAPRVUTk2i7Q4tobrdELrbfrbtTnXOxZfmi6p1CJSXmWU659L9rqOqabtDS6huN4Tutlfkdqs7SEQkhCkERERCWLCHwBS/C/CJtju0hOp2Q+hue4Vtd1CPCYiIyJkF+5GAiIicgUJARCSEBWUIBPNk9maWYmZzzGyNma02s7u89kZmNsvMNno/Y712M7NJ3u9ihZl183cLysfMws1sqZm9671uYWYZ3va97N2iHDOr7b3O8t5P87Pu8jKzhmb2mpmtM7O1ZtY7FPa5mf3Y+3e+ysymmVlUMO5zM3vGzHab2aoSbWXev2Y21lt+o5mNLc26gy4EQmAy+0LgJ865dkAv4DZv++4DZjvn2gCzvdcQ+D208R4TgcervuQKdRewtsTrvwCPOOdaA/uBCV77BGC/1/6It1xN9ijwoXPuAqAzgd9BUO9zM0sC7gTSnXMdCNx+fiTBuc+nAoO+1lam/WtmjYBfAz0JzOf+61PBcUbOuaB6AL2BmSVe3w/c73ddlbi9bwGXA+uBRK8tEVjvPX8SGFVi+f8sV9MeBGaimw1cCrwLGIGrJiO+vu8JzFnR23se4S1nfm/DOW53DLDl6/UH+z7nv3OSN/L24bvAFcG6z4E0YNW57l9gFPBkifb/We50j6A7EqAUk9kHC+9wtyuQASQ453Z6b+0CErznwfT7+Dvwf0Cx97ox8JVzrtB7XXLb/rPd3vsHvOVrohZAPvCs1xX2LzOrS5Dvc+dcLvAQsB3YSWAfLiY09jmUff+e034PxhAICWZWD3gduNs5d7Dkey7wZ0BQnftrZlcCu51zi/2uxQcRQDfgcedcV+AI/+0aAIJ2n8cCQwmEYDOgLt/sMgkJlbl/gzEEgn4yezOrRSAAXnTOzfCa88ws0Xs/EdjttQfL76MPcJWZbQWmE+gSehRoaGanZsgruW3/2W7v/Rhgb1UWXIFygBznXIb3+jUCoRDs+/w7wBbnXL5z7iQwg8C/g1DY51D2/XtO+z0YQyCoJ7M3MwOeBtY65x4u8dbbwKmzAcYSGCs41X6Td0ZBL+BAiUPMGsM5d79zLtk5l0Zgn37inLsBmANc6y329e0+9fu41lu+Rv6l7JzbBWSb2fle02XAGoJ8nxPoBuplZtHev/tT2x30+9xT1v07ExhoZrHeUdRAr+3M/B4MqaQBliHABmAT8Au/66ngbetL4LBwBbDMewwh0Pc5G9gIfAw08pY3AmdLbQJWEjjTwvftKOfv4GLgXe95S2AhkAW8CtT22qO811ne+y39rruc29wFyPT2+5tAbCjsc+C3wDpgFfBvoHYw7nNgGoFxj5MEjvwmnMv+BcZ7258FjCvNunXbCBGREBaM3UEiIlJKCgERkRCmEBARCWEKARGREKYQEBEJYQoBEZEQphAQEQlh/x/JG2f58fcxEQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XniKaWLDAt6u",
        "colab_type": "text"
      },
      "source": [
        "#Wellbore Performance : Pottman and Carpenter\n",
        "\n",
        "## Pwf - Pwh = (rho + k/rho)*h/144\n",
        "\n",
        "### rho = Avg density, k is function of q^2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vr2iUuA7-69V",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "rho = 19.53 #lb/ft3\n",
        "M = 495.66\n",
        "f = 0.002\n",
        "D = 1.66/12"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dsrnxcc_CZhi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "k = (f*(q**2)*(M**2))/(7.4*(10**10)*(D**5))"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pbW_1gw1Edzb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "pwf_out = (rho + k/rho)*2000"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CrmRggW9FOxt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "outputId": "c9b3a77e-4815-4a0b-fa08-d098c218420d"
      },
      "source": [
        "plt.figure(figsize=(7,5))\n",
        "\n",
        "sns.lineplot(q,pwf,label='IPR')\n",
        "sns.lineplot(q,pwf_out,label='TPR')\n",
        "\n",
        "plt.xlabel('Flow Rate Q (STB/day)')\n",
        "plt.ylabel('Pwf at bottomhole node, psia')\n",
        "\n",
        "plt.grid()"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XIuW3-xuFSHJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}